I really like the exploratory/combining elements of the magic system in the computer game Magicka. Can anyone recommend a tabletop game with a similar system?

The system is based on obtaining different effects by combining different "elemental" magics, like water and cold making ice daggers, or water, fire, and lightning making a cloud of electrically charged steam. There are also set spells, like Haste or Revive, based on certain combinations that can be discovered and learned.

What I like is the idea of an experimental magic system that allows for invention and discovery, but I also don't want something completely open; I'm looking for a system that is based on a set of recipes. Maybe something where a character has differing access to/power in different schools/elements based on the build, or where you only have so many slots of a given element/school per day.

6 Answers
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Ars Magica has a set of 5 techniques (to create, to perceive, to change, to destroy, and to control) and 10 forms (animal, air, water, body, plant, fire, image, mind, earth, and power). You can combine the techniques and the forms to quite literally create effects of that combination on the fly, and then research spells for easier/more powerful spells of a more fixed nature.

Depending on your abilities in the forms and techniques, you focus on different ones according to your preference, and effectively has a constrained set of guidelines that allows players to (maybe with more than non-trivial effort) cast practically anything they can think of.

The addition of hidden-to-player spells is actually quite simple.

Don't allow them to read the spellcasting sections of the book.

Create a physical set of cards. Testing will be needed to see how many copies of cards are necessary. You will need, at least, a card for Range, Duration, Target, the 5 Techniques, and the 10 Forms

All spells in the game are spontaneous, and follow spont casting rules (which you may want to adjust for desired power level, or allow the research of formulaic spells per the Faerie-Raised magic rules in HoH:MC)

To cast a spell, players deal out a combo of any number cards in front of them, according to the rules that they have hypothesized. Face down cards should indicate "more" or +1 magnitude. You may or may not want to have order matter.

Fire-Fire-Fire-More-More-Duration-More (Roughly translated as Choose the third guideline at the fifth magnitude Which would create light as bright as direct sunlight on a clear day for Sun duration.

Thus, most of the games would start out being "WTH do all these options do?" as there is plenty to explore, and this formulation will give you an easy way to rule on what amounts to thousands of recipes. Encourage players to document their experiments, as they will be frequently deadly. Use as much of the Ars setting as fits.

The basic concept is similar. Instead of "spells" (fixed, non or barely changeable predefined effects) there are "Spheres" (areas of connected/related aspects of reality). The 9 known Spheres are:

Correspondence

Entropy

Forces

Life

Matter

Mind

Prime

Spirit

Time

Contrary to the system from Ars Magica there is no seperate game statistic on what you can do with a sphere. Instead, this is usually hard-wired into the level of mastery. For example, with Forces 1 you could determine where a cable runs in a wall by feeling the electricity running through it. With Forces 2 you could manipulate that electricity, e.g. hold it off to shut down a machine or spike a surge to blow the safety. With Forces 3 you could convert the electricity directly to another form of energy, e.g. heat or sound. And so on.

Usually, each level of a Sphere allows for these effects:

Perception

Minor manipulation

Convertion (Creation out of nothing if combined with Prime)

Major manipulation

"PHENOMENAL COSMIC POWERS!"

The more powerful effects often require multiple high-level Spheres to be combined. For example, a very powerful effect allows the mage to physically and mentally be at multiple locations by combining the most advanced mastery of:

Each direct application of Sphere magic usually requires a - more or less - difficult roll, but the system allows for the creation of so called "Rotes" that are similar to spells. A Rote is a predefined, easier to learn and use version of a certain magical effect, sometimes with special restrictions or requirements.

Note that the Spheres are virtually omnipotent. Disregarding Paradox and the consequences of vulgar magic for a second, there is basically nothing a mage can't accomplish with the right set of known and mastered Spheres, while - iirc - in Ars Magica there are hard limits like "no resurrection" or "no teleportation" (I may be wrong thou, has been a long time since I've played AM).

I think that Mage is an interesting concept, but in this case I was looking for something less flexible.
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NumeneticsMar 5 '11 at 14:03

@Numenetics: You can easily restrict the flexibility of the system in MtA as well as in AM. There are guidelines (and tables) how to distribute the successes from your casting check (to range, area, strength of the effect, duration, ...) and the level of mastery of a Sphere indicates what you can do. Just as with AM there's no solution for that out of the box and you have to tinker around with the system.
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user660Mar 5 '11 at 14:09

Dresden Files

The DFRPG RPGGeek has an element-based magic system where a given practitioner's mastery of each element is also modified by his ability to gather power, to control it and channel it, and also by his mastery of a particular application - offense or defense for evocation, and a number of different applications for thaumaturgy.

Magic in the Dresden Files universe is taxing and dangerous. Failed rolls to control your magic can cause serious harm to the practitioner, the environment, or bystanders. Not to mention that the Laws of Magic, which prohibit the use of magic to: kill; to alter the minds or bodies of others; to manipulate time; and to pierce the veil of death; are more like Laws of Physics than traffic laws. You can break them (unlike laws of physics) but doing so changes you - you don't have to be caught to suffer the consequences. This makes all but the smallest spells a question: "How important is this spell? Is casting this spell worth what it will / may cost?"

If you're looking for a modern system with a gritty-but-flexible take on magic, I suggest you take a look at The Dresden Files.

The problem with DFRPG magic (which is a great system!) for this application is that it's a "decide effect first, determine mechanical implementation to fit" system, which is the opposite work-flow and knowledge-flow as the OP is specifying.
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SevenSidedDie♦Aug 23 '11 at 20:35

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@Seven - True, but it does satisfy the "experimental magic system that allows for invention and discovery" requirement and like any of the constructive systems here, could have a set of recipes overlaid on it.
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gomadAug 23 '11 at 22:01

GURPS Magic

GURPS Magic has a variant that plays very much like Ars Magica. I can't remember off the top of my head what it's called. Between GURPS Magic and GURPS Thaumatology, there are a bunch of variants that address the constructive flexibility that you seem to be looking for.

The second thing you seem to be looking for is a set of combinations to be discovered. I'd say that's your job as GM to determine which permutations have what effects. So you can decide that, for example, Fire magic + Water magic yields nothing. That's not how I'd do it, though.

Instead, if a player said to me, "I have fire and water skills - I want to combine them to create a steam-cloud spell!" I'd let him research it, and probably send him on a mission to get a scroll or spell focus or something and then let him do it. That way, you don't have to lay out every possible combination in advance!

While donjon doesn't have a list of prescribed recipies, this old indie's game take on magic very much allows the combination of elements and the statement of facts about the world stemming from that combination.

Burning Wheel - Art Magic

If you take a look at The Magic Burner for Burning Wheel, you'll find a number of different magic systems. From variations on the standard Sorcery from the base game to completely different paradigms of magic.

Included in this collection is Art Magic - a much more constructive / combinatorial method of spellcasting in the Burning Wheel system. It bears at least a passing resemblance to the Ars Magica and / or GURPS Collegiate Magic systems.

In this system, like most of the "Lego" style systems that are presented in answers here, you'll have to map out a set of spells to be discovered.